Final answer:
The factored form of (16.72 - 81) is (4.1 + 9)(4.1 - 9), and the factored form of 16x^2 - 81 is (4x + 9)(4x - 9).
Step-by-step explanation:
The first part of the student's question is asking what is the factored form of the expression (16.72 - 81), which is a difference of squares. The difference of squares can be factored using the formula a^2 - b^2 = (a + b)(a - b). We can see that 16.72 can be written as (4.1)^2 and 81 can be written as (9)^2, making the factored form (4.1 + 9)(4.1 - 9), which corresponds to option b).
The second part of the student's question asks for the factored form of 16x^2 - 81. This is also a difference of squares, following the same pattern as above, can be factored as (4x)^2 - (9)^2 = (4x + 9)(4x - 9), which corresponds to option a).